$(50$ points$)$ A W$1039$ rolled steel beam supports a load $P,$ as shown. Knowing that $P=45$kips,$a=10in.$ and ${}_{at}=18$ksi, determine $($a$)$ the maximum value of the normal stress ${}_m$ in the beam, $(b)$ the maximum value of the principal stress ${}_{\text{m}\text{a}\text{x}}$ at the junction of the flange and web, $($c$)$ whether the specified shape is acceptable as far as these two stresses are concerned.

$1$ P

For W$1039$ rolled steel section,

$d=9\mathrm{.}92in,b_f=7\mathrm{.}99in,t_f=0\mathrm{.}530in,$

$t_w=0\mathrm{.}315in,I_x=209i{n}^4,S_x=42\mathrm{.}1i{n}^3$